Introduction to Light Microscopy. (Image: T. Wittman, Scripps)

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1 Introduction to Light Microscopy (Image: T. Wittman, Scripps)

2 The Light Microscope Four centuries of history Vibrant current development One of the most widely used research tools

3 A. Khodjakov et al.

4 Major Imaging Functions of the Microscope Magnify Resolve features Generate Contrast Capture and Display Images

5 An Upright Epifluorescence Microscope

6 Waves vs. Photons vs. Rays Quantum wave-particle duality Rays: photon trajectories Rays: propagation direction of waves

7 Rays are perpendicular to wavefronts

8 Light travels more slowly in matter The speed ratio is the Index of Refraction, n v = c/n n = 1 n > 1 n = 1

9 Refractive Index Examples Vacuum 1 Air Water Cytoplasm ? Glycerol (anhydrous) Immersion oil Fused silica 1.46 Optical glasses Diamond Depends on wavelength and temperature

10 Refraction by an Interface Incident wave 1 r Reflected wave Refractive index n 1 = 1 Speed = c Refractive index n 2 Speed = c/n /n 2 Refracted wave Snell s law: n 1 Sin( 1 ) = n 2 Sin( 2 ) Mirror law: r = 1

11 Which Direction? n 1 n 2 > n 1 Refraction goes towards the normal in the higher-index medium

12 Lenses work by refraction Incident light focus Focal length f

13 Ray Tracing Rules of Thumb (for thin ideal lenses) Parallel rays converge at the focal plane Rays that cross in the focal plane end up parallel f f Rays through the lens center are unaffected

14 Imaging Object f Image d 1 d 2 L 1 L 2 The lens law: 1 L 1 1 L 2 1 f Magnification: M d 2 d 1 L 2 L 1

15 Finite vs. Infinite Conjugate Imaging Finite conjugate imaging (older objectives) Object f 0 Image >f 0 f 0 Infinite conjugate imaging (modern objectives). f 1 Object f 0 Image at infinity Need a tube lens Image f 0 f 0 (uncritical) f 1 Magnification: M f 1 f o

16 Back focal plane Back focal plane f 0 Object f 0 f 0 Rays that leave the object with the same angle meet in the objective s back focal plane

17 The Compound Microscope Exit pupil Eyepiece Primary or intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane

18 The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane

19 The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Back focal plane (pupil) Objective Sample Object plane

20 The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Back focal plane (pupil) Objective Sample Object plane

21 The Compound Microscope Final image Eye Exit pupil Eyepiece Intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane

22 The Compound Microscope Camera Final image Projection Eyepiece Secondary pupil Intermediate image plane Tube lens Objective Sample Back focal plane (pupil) Object plane

23 Eyepieces (Oculars) Features Magnification (10x typical) High eye point (exit pupil high enough to allow eyeglasses) Diopter adjust (at least one must have this) Reticle or fitting for one Eye cups

24 Trans-illumination Microscope Camera Final image plane Imaging path Projection Eyepiece Tube lens Secondary pupil plane Intermediate image plane Illumination path Objective Sample Condenser lens Aperture iris Field lens Field iris Collector Light source Back focal plane (pupil) Object plane (pupil plane) (image plane) (pupil plane) The aperture iris controls the range of illumination angles The field iris controls the illuminated field of view

25 Köhler Illumination Critical Illumination Sample Object plane Aperture iris (pupil plane) Field iris (image plane) Light source (pupil plane) Each light source point produces a parallel beam of light at the sample Uniform light intensity at the sample even if the light source is ugly (e.g. a filament) The source is imaged onto the sample Usable only if the light source is perfectly uniform

26 Conjugate Planes in A Research Microscope

27 How view the pupil planes? Two ways: Eyepiece telescope Bertrand lens

28 By far the most important part: the Objective Lens Each major manufacturer sells different categories of objectives. What are the important distinctions?

29 Working Distance In general, high NA lenses have short working distances However, extra-long working distance objectives do exist Some examples: 10x/0.3 WD = 15.2mm 20x/0.75 WD = 1.0mm 100x/1.4 WD = 0.13mm

30 The focal length of a lens depends on the refractive index Refractive index n f 1/(n-1) Focal length f

31 and the refractive index depends on the wavelength ( dispersion ) Glass types

32 Chromatic aberration Different colors get focused to different planes Not good

33 Dispersion vs. refractive index of different glass types Refractive index Abbe dispersion number (Higher dispersion )

34 Achromatic Lenses Use a weak negative flint glass element to compensate the dispersion of a positive crown glass element

35 Achromats and Apochromats Focal length error Wavelength Apochromat ( 3 glass types) Achromat (2 glass types) Simple lens

36 Correction classes of objectives Achromat (cheap) Fluor semi-apo (good correction, high UV transmission) Apochromat (best correction) Correction for other (i.e. monochromatic) aberrations also improves in the same order

37 Curvature of Field Focal plane Focal surface Tube lens objective sample Focal surface

38 Plan objectives Corrected for field curvature More complex design Needed for most photomicrography Plan-Apochromats have the highest performance (and highest complexity and price)

39 In phase Interference constructive interference + = Opposite phase + = destructive interference

40 Diffraction by a periodic structure (grating)

41 Diffraction by a periodic structure (grating) d In phase if: d Sin( ) = m for some integer m

42 Diffraction by an aperture drawn as waves Light spreads to new angles Larger aperture weaker diffraction

43 Diffraction by an aperture drawn as rays The pure, far-field diffraction pattern is formed at distance Tube lens or can be formed at a finite distance by a lens Objective pupil Intermediate image as happens in a microscope

44 The Airy Pattern = the far-field diffraction pattern from a round aperture Height of first ring 1.75% Airy disk diameter d = 2.44 f/d (for small angles d/f) d f

45 Objective Aperture and Resolution Tube lens Intermediate image plane Diffraction spot on image plane = Point Spread Function Sample Back focal plane aperture

46 Objective Aperture and Resolution Tube lens Intermediate image plane Diffraction spot on image plane = Point Spread Function Sample Back focal plane aperture

47 Objective Aperture and Resolution Tube lens Intermediate image plane Diffraction spot on image plane = Point Spread Function Sample Back focal plane aperture

48 Objective Aperture and Resolution Tube lens Intermediate image plane Diffraction spot on image plane (resolution) Sample Back focal plane aperture Image resolution improves with aperture size Numerical Aperture (NA) NA = n sin( ) where: = light gathering angle n = refractive index of sample

49 Numerical Aperture 100X / 0.95 NA = X / 0.20 NA = 11.5

50 Immersion Objectives NA cannot exceed the lowest n between the sample and the objective lens NA >1 requires fluid immersion NA can approach the index of the immersion fluid Oil immersion: n max NA 1.4 ( for TIRF) Glycerol immersion: n 1.45 (85%) max NA 1.35 (Leica) Water immersion: n 1.33 max NA 1.2

51 Resolution Ernst Abbe s argument (1873) Consider a striped sample a diffraction grating Back focal plane Objective lens Sample Condenser d b Diffracted beams d sin(b) = Smaller d larger b Light source Consider first a point light source If b >, only one spot makes it through no interference no image formed Resolution (smallest resolvable d): dmin = sample/sin( ) = /n sin( ) = /NA

52 (Abbe s argument, continued) Now consider oblique illumination (an off-axis source point): One spot hopelessly lost, but two spots get through interference image formed! d bout bin d [sin(bin) + sin(bout) ] = Two spots get through if bout < and bin <. Resolution (smallest resolvable d) with incoherent illumination (all possible illumination directions): dmin = /(NAobj + NAcondenser ) /2 NA if NAcondenser NAobj ( Filling the back focal plane )

53 Aperture, Resolution & Contrast Can adjust the condenser NA with the aperture iris Imaging path Intermed. image Tube lens Illumination path Back aperture Objective Sample Condenser lens Aperture iris Field lens Field iris Collector Light source Q: Don t we always want it full open?? A: No Why? Tradeoff: resolution vs. contrast

54 NA and Resolution High NA Objective Low NA Objective

55 Alternate Definitions of Resolution As the Full Width at Half Max (FWHM) of the PSF FWHM /NA As the diameter of the Airy disk (first dark ring of the PSF) = Rayleigh criterion (Probably most common definition) Airy disk radius 0.61 /NA

56 Objective Types Plan or not Field flatness Basic properties Magnification Numerical Aperture (NA) Infinite or finite conjugate Cover slip thickness if any Immersion fluid if any Correction class Achromat Fluor Apochromat Phase rings for phase contrast Positive or negative Diameter of ring (number) Special Properties Strain free for Polarization or DIC Features Correction collar for spherical aberration Iris Spring-loaded front end Lockable front end

57 micro.magnet.fsu.edu Further reading Douglas B. Murphy Fundamentals of Light Microscopy and Electronic Imaging James Pawley, Ed. Handbook of Biological Confocal Microscopy, 3rd ed. Ron Vale / Mats Gustafsson Acknowledgements

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